Question

Explain circular permutation with the help of an example

Answer 1

Nice question ask your teacher

Answer 2

Answer is given below.

Step-by-step explanation:

Given,

Circular permutation with the help of an example.

Circular permutation:

                                  Permutation in a circle is called circular permutation. The number of ways to arrange distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is. The number is instead of the usual factorial since all cyclic permutations of objects are equivalent because the circle can be rotated.

If we consider a round table and $3$ persons then the number of different sitting arrangement that we can have around the round table is an example of circular permutation. Now the circular part$!$ ... So for $n$ elements, circular permutation $=\frac{n!}{n}=(n-1)!$

Example:

Find the number of ways in which $5$people $A,B,C,D,E$ can be seated at a round table, such that

(i) $A$ and $B$ must always sit together.

Solution: If we wish to seat $A$ and $B$ together in all arrangements, we can consider these two as one unit, along with $3$ others. So effectively we’ve to arrange $4$ people in a circle, the number of ways being $(4-1)!$ or $6$. Let me show you the arrangements:

But in each of these arrangements, $A$ and $B$ can themselves interchange places in $2$ ways. Here’s what I’m talking about:

Therefore, the total number of ways will be $(6\times 2=12)$